The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time–space propagation of such diseases using a diffusion–reaction epidemiological model of the susceptible–exposed–infected–recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.

正如最近的大流行所证明的那样，对 COVID-19 等疾病传播的实时预测和估计至关重要。这项工作涉及使用易感-暴露-感染-恢复 (SEIR) 类型的扩散-反应流行病学模型对此类疾病的时空传播进行分布式参数估计。状态估计基于对每单位时间和宿主空间域的感染和死亡人数的连续测量。观测器设计方法基于正定矩阵参数化一类李亚普诺夫泛函，以稳定估计误差动力学。因此，稳定性条件可以表示为一组矩阵不等式约束，可以使用平方和 (SOS) 和标准半定规划 (SDP) 工具对其进行数值求解。根据与 2020 年 3 月法国情况相对应的简化案例研究分析了观察者的表现，并显示出可喜的结果。